Problem: Nauuo is a girl who loves playing chess.

One day she invented a game by herself which needs n chess pieces to play on a m× m chessboard. The rows and columns are numbered from 1 to m. We denote a cell on the intersection of the r-th row and c-th column as (r,c).

The game's goal is to place n chess pieces numbered from 1 to n on the chessboard, the i-th piece lies on (r_i,\,c_i), while the following rule is satisfied: for all pairs of pieces i and j, |r_i-r_j|+|c_i-c_j|≥|i-j|. Here |x| means the absolute value of x.

However, Nauuo discovered that sometimes she couldn't find a solution because the chessboard was too small.

She wants to find the smallest chessboard on which she can put n pieces according to the rules.

She also wonders how to place the pieces on such a chessboard. Can you help her?

Input

The only line contains a single integer n (1≤ n≤ 1000) — the number of chess pieces for the game.

Output

The first line contains a single integer — the minimum value of m, where m is the length of sides of the suitable chessboard.

The i-th of the next n lines contains two integers r_i and c_i (1≤ r_i,c_i≤ m) — the coordinates of the i-th chess piece.

If there are multiple answers, print any.

Examples

Input


2


Output


2
1 1
1 2

Input


4


Output


3
1 1
1 3
3 1
3 3

Note

In the first example, you can't place the two pieces on a 1×1 chessboard without breaking the rule. But you can place two pieces on a 2×2 chessboard like this:

<image>

In the second example, you can't place four pieces on a 2×2 chessboard without breaking the rule. For example, if you place the pieces like this:

<image>

then |r_1-r_3|+|c_1-c_3|=|1-2|+|1-1|=1, |1-3|=2, 1<2; and |r_1-r_4|+|c_1-c_4|=|1-2|+|1-2|=2, |1-4|=3, 2<3. It doesn't satisfy the rule.

However, on a 3×3 chessboard, you can place four pieces like this:

<image>

Solution (in CPP):

Solution:
#include <bits/stdc++.h>
using namespace std;
int main() {
  int n, i, j, pi, pj;
  scanf("%d", &n);
  int size = (n / 2) + 1;
  int m[size][size];
  int arr[n + 1];
  for (i = 0; i < n + 1; i++) {
    arr[i] = 0;
  }
  for (i = 0; i < size; i++) {
    for (j = 0; j < size; j++) {
      m[i][j] = 0;
    }
  }
  m[0][0] = 1;
  m[size - 1][size - 1] = n;
  arr[1] = 1;
  arr[n] = 1;
  printf("%d\n", size);
  int count = 2;
  int next = n - 1;
  pi = size - 2;
  while (pi >= 0) {
    if (!arr[next]) m[size - 1][pi] = next;
    arr[next] = 1;
    next--;
    pi--;
    count++;
  }
  pi = 1;
  int nextm = 2;
  while (nextm <= next) {
    if (!arr[nextm]) m[0][pi] = nextm;
    arr[nextm] = 1;
    nextm++;
    pi++;
  }
  for (i = 0; i < size; i++) {
    for (j = 0; j < size; j++) {
      if (m[i][j]) printf("%d %d\n", i + 1, j + 1);
    }
  }
}